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Vector Algebra

Question
CBSEENMA12033984
Wired Faculty App

Find the unit vector in the direction of vector PQ with rightwards arrow on top, where P and Q are the points (1, 2, 3) and (4, 5, 6) respectively.

Solution
Given points are P (1. 2. 3), Q (4. 5, 6)

therefore space space space space space PQ with rightwards arrow on top space equals space straight P. straight V. space of space straight Q space minus space straight P. straight V. space of space straight P space space space space space space space space space space space space space space space space space equals space left parenthesis 4 straight i with hat on top space plus space space 5 straight j with hat on top space plus space 6 straight k with hat on top right parenthesis space minus left parenthesis straight i with hat on top plus 2 straight j with hat on top plus 3 straight k with hat on top right parenthesis space equals space 3 straight i with hat on top space plus space 3 straight j with hat on top space plus space 3 straight k with hat on top therefore space space space space open vertical bar PQ with rightwards arrow on top close vertical bar space equals space square root of 9 plus 9 plus 9 end root space equals space square root of 27 space equals space square root of 9 space cross times 3 end root space equals space 3 square root of 3
Unit vector in the direction of PQ is = fraction numerator PQ with rightwards arrow on top over denominator open vertical bar PQ with rightwards arrow on top close vertical bar end fraction
                                equals space fraction numerator 1 over denominator 3 square root of 3 end fraction left parenthesis 3 straight i with hat on top space plus space 3 straight j with hat on top space plus space 3 space straight k with hat on top right parenthesis space equals space fraction numerator 1 over denominator square root of 3 end fraction straight i with hat on top space plus space fraction numerator 1 over denominator square root of 3 end fraction straight j with hat on top space plus fraction numerator 1 over denominator square root of 3 end fraction straight k with hat on top

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